... 2006, 497–550.the electronic journal of combinatorics 15 (2008), #N16 5Necklace bisection with one cut less than neededG´abor Simonyi∗Alfr´ed R´enyi Institute of MathematicsHungarian Academy ... specifytwo disjoint sets D1, D2of the types of beads with D1∪ D2= ∅, it will always bepossible to cut the necklace (with k − 1 cuts) so that the first thief gets more ofthose types of ... the following consequence. We usethe phrase necklace bisection with the same meaning as in [2], i.e., it is a collection of cutstogether with a bipartition of the segments thus created. We also...